Read the type of material you mean to write, for a wide range of ages, levels of seriousness, audiences, classics.
This is a bit hard to decipher. I guess if I was Neil Gaiman, I'd read lots of stuff about myths, folk tales, and legends. This is not hard to do at a wide range of ages, seriousness, audiences, and classics. If I was Stephen King, it's hard to find horror for a wide range of the above-mentioned criteria, unless you wanna read the Goosebumps books, but I don't think he has debased himself to that. If you're Audrey Niffenegger, what do you read? Dean Koontz and Louis L'Amour? Seems an odd combination, but writers are an odd people. Myself, I've been sticking to genre novels pretty cleanly most of my life. I had bouts where I'd pick books on subject alone (like anything involving cats, anything involving Star Trek), but mostly I stay within Science Fiction, and things with talking animals (I don't know either, look at my tag cloud on LibraryThing. The evidence speaks for itself.)
I think it's important to read what you want to write for several reasons. One, finding out the current status of the publishing industry in this type of writing. Two, reading stories gives way to ideas for writing stories, it's a great resource. Three, learn how to write what you want to write. If you notice the space-ship epics out there don't have a lot of soliloquys, and yours does, you may want to rethink that.
The caveat to this is I remember reading something in Neil Gaiman's journal when he wrote American Gods, he held off on reading some books in fear that they would be similar to his. I guess he didn't want to accidentally plagiarize something, even subconsciously, or have an idea that wasn't his own. That's both stupid and a good idea, because how are you supposed to read what you mean to write, if you can't read it.